4n^2-7n-22=0

Simple and best practice solution for 4n^2-7n-22=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 4n^2-7n-22=0 equation:


Simplifying
4n2 + -7n + -22 = 0

Reorder the terms:
-22 + -7n + 4n2 = 0

Solving
-22 + -7n + 4n2 = 0

Solving for variable 'n'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-5.5 + -1.75n + n2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -1.75n + 5.5 + n2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -1.75n + n2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -1.75n + n2 = 0 + 5.5
-1.75n + n2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-1.75n + n2 = 5.5

The n term is -1.75n.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75n + 0.765625 + n2 = 5.5 + 0.765625

Reorder the terms:
0.765625 + -1.75n + n2 = 5.5 + 0.765625

Combine like terms: 5.5 + 0.765625 = 6.265625
0.765625 + -1.75n + n2 = 6.265625

Factor a perfect square on the left side:
(n + -0.875)(n + -0.875) = 6.265625

Calculate the square root of the right side: 2.503123049

Break this problem into two subproblems by setting 
(n + -0.875) equal to 2.503123049 and -2.503123049.

Subproblem 1

n + -0.875 = 2.503123049 Simplifying n + -0.875 = 2.503123049 Reorder the terms: -0.875 + n = 2.503123049 Solving -0.875 + n = 2.503123049 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + n = 2.503123049 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + n = 2.503123049 + 0.875 n = 2.503123049 + 0.875 Combine like terms: 2.503123049 + 0.875 = 3.378123049 n = 3.378123049 Simplifying n = 3.378123049

Subproblem 2

n + -0.875 = -2.503123049 Simplifying n + -0.875 = -2.503123049 Reorder the terms: -0.875 + n = -2.503123049 Solving -0.875 + n = -2.503123049 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + n = -2.503123049 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + n = -2.503123049 + 0.875 n = -2.503123049 + 0.875 Combine like terms: -2.503123049 + 0.875 = -1.628123049 n = -1.628123049 Simplifying n = -1.628123049

Solution

The solution to the problem is based on the solutions from the subproblems. n = {3.378123049, -1.628123049}

See similar equations:

| x^3-7x^2-16x+112=0 | | 6(3+x)=24 | | 4n^2-7n+22=0 | | 6c^3+5c^2-25c^2=0 | | 3x=4+2x | | R=(15.00-0.25*R)(0.12) | | 459/x+3c/x=4d+23p | | (D^3+3D^2+3D+1)y=8sinx | | 7+10=9*8 | | x=3-3y4y=x+11 | | (6p+4)/6=(4p-8)/3 | | 3m-m/3m | | 8/7a=-72/13 | | 6x+11y=180 | | -18+24=m-5 | | 6x+19+x=180 | | -16r^3+10r= | | 11y+4x+16=180 | | 20+8x=84 | | 11s+9-3a=-7 | | x=4+0.6 | | 4x=x^2-70 | | 459-3b/x=4d+22P | | 2(1+5x)=-98 | | 0=-t^4+9t^2+400 | | 459-3x/A=4d+22P | | 6x+10+6x=13 | | 7-i/3-8i | | 2d^2+9h=0 | | 4(x-3)=37 | | 4n-1=3x+2 | | y-12+3y-8=180 |

Equations solver categories